Evaluation of Long-Dated Investments under Uncertain Growth Trend, Volatility and Catastrophes

Because of the uncertainty about how to model the growth process of our economy, there is still much confusion about which discount rates should be used to evaluate actions having long-lasting impacts, as in the contexts of climate change, social security reforms or large public infrastructures for example. In this paper, we take this critique seriously by assuming that the random walk of economic growth is affected by some parametric uncertainty. We show that the same arguments proposed in the literature to justify a decreasing term structure for the safe discount rate also apply to justify an increasing term structure for the risk premium. It also implies that, under the assumption that the cumulants of the distribution of growth are statistically independent, the discount rate is increasing with maturity if and only if the beta of the investment is larger than half of relative risk aversion. Another important consequence of parametric uncertainty is that the risk premium is not proportional to the beta of the investment. We apply these general results to the case of an uncertain probability of macroeconomic catastrophes à la Barro (2006), and to the case of an uncertain trend or volatility of growth à la Weitzman (2007). Finally, we apply our findings to the evaluation of climate change policy. We argue in particular that the beta of actions to mitigate climate change is relatively large, so that the term structure of the associated discount rates should be increasing.